Derivation of s= u+ 1/2 at2

Question

asked Jun 17, 2022 184k views

1 Answer

Yogesh Patil · Answer 1 · 2022-06-22T12:20:53+0000

We know that

Velocity is given by the rate of change of position w.r.t time

$\\ \sf\longmapsto v=(dx)/(dt)$

$\\ \sf\longmapsto vdt=dx$

Now we can see in above v is not independent of t .So we replace the value of v by v=u+at and we get

$\\ \sf\longmapsto (u+at)dt=dx$

$\\ \sf\longmapsto u{\displaystyle{\int}_0^t}dt+a{\displaystyle{\int}_0^t}dt={\displaystyle{\int}^x_(x_0)}dx$

$\\ \sf\longmapsto ut+(1)/(2)at^2=(x-x_0)$

$\\ \sf\longmapsto x=x_0+ut+(1)/(2)at^2$